Express $x^{2} + 8 x + 3$ in the form $(x + p)^{2} + q$ . What is the minimum value of the expression?

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More Quadratic functions and inequalities questions

Find the set of values of $k$ for which the equation $x^{2} + k x + 4 = 0$ has real roots.
Find the set of values of $k$ for which the equation $x^{2} + k x + 9 = 0$ has real roots.
Find the set of values of $k$ for which the equation $x^{2} + k x + 16 = 0$ has real roots.
Find the set of values of $k$ for which the equation $x^{2} + k x + 25 = 0$ has real roots.
Find the set of values of $k$ for which the equation $x^{2} + k x + 36 = 0$ has real roots.
Find the set of values of $k$ for which the equation $x^{2} + k x + 1 = 0$ has real roots.